Question

which triangle is a translation of triangle p? graph of coordinate plane with triangles a, b, c, d, and p
options: triangle a, triangle b, triangle c, triangle d

Explanation:

A translation of a figure preserves its shape, size, and orientation, only changing its position. Triangle \( P \) is a right - angled triangle with a specific orientation (right angle at the bottom - left, legs along the grid lines).

• Triangle \( A \): It is an isosceles triangle (not a right - angled triangle like \( P \)), so it can't be a translation of \( P \).
• Triangle \( B \): It has the same shape (right - angled, same proportions of legs), same size, and same orientation as triangle \( P \). It appears to be a horizontal translation of \( P \) (moved to the right without any rotation or reflection).
• Triangle \( C \): Its orientation of the right angle and the slope of the hypotenuse are different from \( P \) (it is a reflection or rotation - modified version compared to \( P \)).
• Triangle \( D \): Its orientation and the relative lengths of the legs (compared to the grid) are different from \( P \) (it is a reflection or rotation - modified version compared to \( P \)).

Answer:

triangle B